Google is testing asking searchers to sign in within the AI Mode response. Google shows a big Google super logo and a sign in button that says "Sign in to save your..."
This test was spotted by Sachin Patel who posted about this on X and on SEW - here is that screenshot:
I can't replicate this but I assume this lets you save the results to your Google account and/or makes the next prompts smarter related to SEO tools queries.
Forum discussion at X.